Multiply the following complex numbers: $({-1-3i}) \cdot ({1-i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-3i}) \cdot ({1-i}) = $ $ ({-1} \cdot {1}) + ({-1} \cdot {-1}i) + ({-3}i \cdot {1}) + ({-3}i \cdot {-1}i) $ Then simplify the terms: $ (-1) + (1i) + (-3i) + (3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -1 + (1 - 3)i + 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -1 + (1 - 3)i - 3 $ The result is simplified: $ (-1 - 3) + (-2i) = -4-2i $